Problem: Solve for $x$ and $y$ using elimination. ${-2x+2y = 2}$ ${2x-5y = -23}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-3y = -21$ $\dfrac{-3y}{{-3}} = \dfrac{-21}{{-3}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x+2y = 2}\thinspace$ to find $x$ ${-2x + 2}{(7)}{= 2}$ $-2x+14 = 2$ $-2x+14{-14} = 2{-14}$ $-2x = -12$ $\dfrac{-2x}{{-2}} = \dfrac{-12}{{-2}}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {2x-5y = -23}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(7)}{= -23}$ ${x = 6}$